Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C22 |
| direct product | C7×#13469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2065 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| prime radical | C2×C7×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ C7×#405 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,16,20,15,21,14,34)(10,22,11,26,25,35,30,37)(12,31,33,39,13,32,27,19)(17,29,38,23,36,28,18,24);(8,10,12,23,14,11,27,28,15,25,13,24,16,30,33,29)(9,17,19,22,20,18,31,37,21,36,39,35,34,38,32,26);(8,11)(9,18)(10,14)(12,24)(13,23)(15,30)(16,25)(17,20)(19,35)(21,38)(22,39)(26,32)(27,28)(29,33)(31,37)(34,36)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 6457);